# Full text of "Analytical Mechanics"

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IMPULSE AND MOMENTUM 257 rest in 0.1 second by closing a valve at the lower end. Find the increase of pressure produced near the valve in both the C.G.S. and the British units. The length of the pipe is 500 meters. 4. A jet of water strikes a blade of a turbine normally. If the velocity of the jet is 150 feet per second, find the pressure it exerts on the blade, (a) when the blade is fixed; (b) when it has a velocity of 50 feet per second along the jet. 6. Figure 120a represents a horizontal trough with smooth vertical walls. The stream is supposed to have the same speed, 6 miles per hour, in all three parts of the trough. The stream in C is one-third of that-in B. Find the force on the wall EC. The cross-section of the stream in A is 5 feet by 3 feet. 6. In the preceding problem suppose the branch C to be closed. FIG. 120. 7. A stream of water flowing in a horizontal direction is divided into two equal streams, as shown in Fig. 120b. Supposing the velocity of the water to remain unchanged derive an expression for the force on the obstacle, and discuss it for special values of 9. 8. In the preceding problem suppose the velocity of the stream to be 5 miles per hour, its cross-section before it is divided to be 4 feet by 2 feet, and 8 = 120°. 9. In the preceding problem take 9 — IT. 10. In (8) take d = ^f - jL 11. In (8) take0 = 2?r. 12. A machine gun delivers 500 bullets per minute with a velocity of 1800 feet per second. If the bullets weigh 0.5 ounce each find the average force on the carriage of the gun. 13. A train scoops up 1500 pounds of water into the tender from a trough 500 yards long while making 50 miles per hour. Find the added resistance to the motion of the train.